At the level of generality presented in the question, it is impossible to know with any meaningful level of comfort, which state's laws regarding punitive damages caps will apply, even if there are prior precedents addressing a similar issue, since the determination is so dependent upon a rich set of relevant facts.
Does Federal Or State Law Apply?
In a diversity case, under what is known as the Erie doctrine, after the U.S. Supreme Court case that established it, a federal district court sitting in diversity applies the substantive law of the state in which it is located (including its choice of law rules) and federal procedural law.
A variety of subsequent cases have clarified (or at least made more specific) what counts as substantive law, and what counts as procedural law. A 2018 law review article (open access) uses a five page long flow chart to explain the rule. A simplified partial page flowchart regarding whether state or federal law applies can be found here.
To cut a long analysis short, punitive damage limitations generally count as substantive law under this test.
So, the question of which state's law to apply to punitive damages caps in a diversity case brought in a U.S. District Court in Texas is precisely the same as the question faces by a Texas state court regarding which state's law to apply.
Choice Of Law Analysis At The State Level
In general, a state court (or a federal court sitting in diversity) applies the law of the state in which it is located unless a party argues that under choice of law principles that another state's law should apply, and that party shows that the law of the state whose law is proposed is different from the law of the state where the case is being tried.
Historically, there were rigid rules that provided that in particular kinds of cases, a particular state's law would apply. Some of those historical rules continue to have full force.
For example, the substantive real property law of the state where real property is located almost always applies.
But, in other cases, a more vague modern rule for choice of law applies. This is the rule that the law of the state with the most significant relationship to the issue to be decided should apply. Different issues in the same case may end up being governed by different laws as a result.
Among the factors to be considered in applying a most significant relationship test are:
The place where the event giving rise to the claim occurred.
The interest of the state where the person who was harmed resides in controlling the amount of compensation that the person harmed received.
The interest of the state where the person who caused the harm resides in encouraging or discouraging business activity that may hurt others.
The interest of the state where the insurance company paying some or all of the claim is located in not driving up insurance premiums.
The inquiry in this multi-factor balancing test is usually extremely fact intensive.
The practical effect of the most significant relationship test has been to make the ultimate decision less predictable and to make it more likely that a judge will decide that the forum state's law will apply. Under the historical rule, about two-thirds of requests to apply a non-forum state's law were granted. Under the modern rule, about one-third of such requests are granted.
A law review article from 1987 spells out the choice of law rules in Texas at the time which have probably become somewhat looser since that time that it was written. The article is James P. George, Choice of Law Outline for Texas Courts, 18 Tex. Tech L. Rev. 785 (1987). Available at: https://scholarship.law.tamu.edu/facscholar/255
A short article looking at the case law for choice of law cases with regard to punitive damages can be found here. It opens by observing that:
The United States Supreme Court has repeatedly acknowledged that while
states are afforded discretion over the imposition of punitive
damages, state law is still subject to "procedural and substantive
constitutional limitations on these awards." State Farm Mut. Auto.
Ins. Co. v. Campbell, 538 U.S. 408, 416 (2003). Relying on the Due
Process Clause, the Court has provided some basis for determining
which state's law applies to the punitive damages question and what
conduct is subject to punitive liability. In Phillips Petroleum Co. v.
Shutts, for example, the Supreme Court held that "for a State's
substantive law to be selected in a constitutionally permissible
manner, that State must have a significant contact or significant
aggregation of contacts, creating state interests, such that choice of
its law is neither arbitrary nor fundamentally unfair." Phillips
Petroleum Co. v. Shutts, 472 U.S. 797, 818 (1985) (internal quotation
marks and citation omitted). The Court has also made clear that
"[e]lementary notions of fairness" require that a defendant must be
given "fair notice" of what conduct is subject to punitive damages, as
well as the severity of the penalty that may be imposed. BMW of N.
Am. v. Gore, 517 U.S. 559, 574 (1996).
It also observes in an analysis that should be taken with a grain of salt, because it comes from a law firm that defends companies that are usually defendants in product liability cases rather than plaintiffs and is not written by a neutral party:
a growing number of courts have begun to recognize that an analysis of
the Restatement factors points to the application of defendants' home
jurisdictions' laws to the issue of punitive damages. See, e.g.,
Kirchman v. Novartis Pharm. Corp., No. 8:06- cv-1787-T-24-TBM, 2014 WL
2722483, at *4 (M.D. Fla. June 16, 2014) (applying the law of New
Jersey to punitive damages claim because that state "is the place of
injury-causing conduct," i.e., the state "where Novartis made its
corporate decisions regarding the labeling, packaging and warning of
the drugs, which Plaintiff alleges caused Mr. Kirchman's osteonecrosis
of the jaw") (citation omitted); Williams v. Novartis Pharm. Corp., 15
F. Supp. 3d 761, 768 (S.D. Ohio 2014) ("When a plaintiff seeks
punitive damages against a manufacturer in a products liability case
based on a 'failure to warn' theory, the focus, for purposes of a
choice-of-law analysis, needs to be on the place where the defendant's
alleged corporate misconduct occurred."); Braun, 2014 WL 345246, at *5
(California law applied to punitive damages claims against infant
sling manufacturer because defendant "designed its products in
California" and therefore "all of the actions that would form the
basis for punitive damages occurred there"); Dopson-Troutt v. Novartis
Pharm. Corp., No. 8:06-CV-1708-T-24-EAJ, 2013 WL 3808205, at *4 (M.D.
Fla. July 22, 2013) ("The Court agrees with the reasoning of the other
courts who have found that" the Restatement principles "support
applying New Jersey law to the punitive damages issue in this case"
because "the basic policy underlying punitive damages is to punish and
deter [the defendant], whose conduct occurred in New Jersey . . . .")
(internal quotation marks and citation omitted). For example, in Irby,
a Virginia plaintiff alleged that he developed osteonecrosis of the
jaw after ingesting the drug Zometa, manufactured by Novartis. Irby,
2011 WL 5835414, at 2. The parties stipulated that Virginia law
governed the plaintiff's compensatory claims for failure to warn,
defective design, breach of implied warranty, negligence, and consumer
fraud. They disagreed, however, on which state's law should govern
plaintiff's punitive damages claim. Virginia law caps punitive damages
at $350,000, while New Jersey law bars them completely in cases
involving FDA-approved drugs. Plaintiff argued Virginia law should
apply as the place of injury, while Novartis argued that the law of
New Jersey should apply because its principal place of business is
located in that state.
To some extent, these choice of law principles apply even in cases where there are arguably procedural rules that apply, rather than merely blindly following a federal procedure and state substantive distinction. Wikipedia's entry on the Erie doctrine concludes in part by stating:
Erie has gone in a newer and
even more complicated direction than the previous controlling cases,
and that instead of selecting either federal or state law for a case,
the federal court may be required to somehow blend federal and state
law, depending on the issue. This is quite frustrating for those who
wish to have a black-letter rule that will point them to the answer.
However, the possibility of blending in Erie does not open up an
infinitude of possibilities.
But even in the context here where it is clear that state law rather than federal law applies, the determination of which state's law applies is itself involved and is frustratingly indeterminate.