It really depends how the tag line is presented. For example, "BigCo" may be an unregistrered (TM) or a Registered Trademark (R), but "big co" is not a registered mark. So if NewCo could have an actor say your tag line in all spoken advertisements and then when served a trademark dispute claim "You thought we said 'BigCo? We said 'big co'." In print they could say:
NewCo - (Like [a] big co, only newer).
The article "a" is added so that it grammatically flows but the argument is that NewCo is saying they are big corperation or company (abbreviated co) but are newer. BigCo may be a subset of big corperations, but so is GiantCo and NovaCo, which are not direct competition. In New Co's market.
Another play is to move around word or refernce concepts so that there is a generic boast but any consumer would know the dig is directed a competators. For example, say McDonalds and Burger King release the following two claims in their ads:
McDonald's: Come to McDonald's, the true king of burgers.
Burger King: Come to Burger King, where we never clown around with our customers.
In both cases, the statements use generic terms to poke fun at their competator's brand without saying the name directly. Everyone knows that Burger King's mascot is a king of burgers while McDonald's mascot is a clown, and that the jabs are invoking claims but the ads aren't directly featuring either company's trademarks. Here this is puffery as both claims are subjective in the eyes of a consumer. It's highly unlikely that either company would be in any legal challenge. Also because we all know Wendy's is the true sass queen of the fast food burger joints... and their popular "Where's the Beef?" ad campaign featured a fictional competator which advertised a hamburger with a large bun and a comically small patty and cheese slice. At the time, McDonald's (and Burger King) focused strongly on the bun of their product with terms describing it as "Big and Fluffy" as it was assumed the beef was going to be in the bun. The point was summed up in the Wendy's commercial when the competator was shown to have a single golden arch as it's logo, evoking similar images to McDonald's famous logo. The campaign was so sucessful that 1984's presidential campaign would see the slogan adopted by Walter Mondale during the primaries, and the actress who played the old lady asking the question would feature in a Prego (spaghetti sause) commercial which advertised it's beef blend with her saying "I've found it!" Another example of parody and word play being used is how you answer the question: Which company sells batteries with a toy pink bunny beating a drum that lasts forever because of the battery? If you're in the United States, you would say "Energizer". In Europe the answer is "Duracell". The Energizer Bunny was a parody of an iconic Duracell Bunny which was used 15 years previous. Despite the campaign concluding, Duracell sued but settled for splitting the trademark so Energizer would have the trademark in the US and Duracell would have it everywhere else. Part of the reason the case didn't go to trial was Duracell's lapse of use of the character and several differneces: Energizer's character wore prominant sunglasses, sandles, and was a lone individual while Duracell's bunnies wore a yellow shirt and were a species (It's THE one and only Energizer Bunny in all commercials vs. A group of (or one of a group of) several Duracell Bunnies in all commercial).
Another case is say NewCo releases an ad where it states that in a recenty trade magazine, NewCo's products were found to be more Modern than BigCo's products and then mad your slogan. Here, it's acceptable because they cite an trade source that did a side by side comparison between to products on objective merits (or customer subjective preference) and used the findings. One famous campaign of this nature is The Pepsi Challenge which feature a single sip blind taste test where the customers overwhelmingly chose the product revealed to be Pepsi over Coca-Cola (Coke). The ad worked because when drinking a sip, consumers would typically prefer a sweeter flavor, which Pepsi had over Coke.. However, if allowed to consume the whole can, Coke would bring in a slightly better result. Pepsi could set up anywhere and give the test, film it, cut the examples of customers choosing coke, and run the ad with their commentator's product displayed because they could not show the test results without a fair use of their competitor's product. Coke did not take this lying down and did their own counter marketing digs, such as releasing a campaign button which read "I selected Coke in the Pepsi Challenge." (Pepsi Challenge was a trade mark for the campaign but Coke could use it because they were advertising the people who were proud because they made the "right" choice in Coke's view. As it was a study, Coke could tout the results, including the pride of their loyal customers who didn't take the bait.) If BigCo was established in 1887 and NewCo was established in 2007, and they featured the same product, then your above slogan has an objective statement of fact and is not puffery. Furthermore, while objective, it would not necessarily be damaging as BigCo can counter that 100 years of experience in the market and nostailgic pleas could counter the illusion of moderness. BigCo would be better served by pointing out that you should trust the time tested BigCo over some young upstart like NewCo than actually suing NewCo, who could not only have a valid defense but spin the PR as BigCo being so afraid of a competitor that they would resort in uncompetative practices to get rid of competition. (Suing a company out of Buisness is not competitive as opposed to product sales. BigCo would only sue a smaller new company if it feared the new company would actually be able to take a big bight out of their market share... and this is over a correctly stated 120 year age difference between the two... which would imply BigCo is old and rigid while NewCo is hip and down with the kids).