Firstly, it should be noted that unlike the 27th Amendment, there is little chance that the Congressional Apportionment Amendment would be ratified today. Kentucky was the 11th state to ratify, back in 1792, and there have been zero additional ratifiers since. Frankly getting more Congressmen isn't something people are clamoring for - can't imagine why :)
More importantly, if the Amendment were to somehow be ratified, it would need to be reconciled with the Apportionment Act of 1911. In 1911, Congress decided for itself, consistent with its own rules and powers, that the chamber would be limited to 435 members.
James Madison writes about this very issue in Federalist Paper #55. He describes the tension between a Congress that is too large and too small as follows:
Sixty or seventy men may be more properly trusted with a given degree of power than six or seven. But it does not follow that six or seven hundred would be proportionably a better depositary. And if we carry on the supposition to six or seven thousand, the whole reasoning ought to be reversed. The truth is, that in all cases a certain number at least seems to be necessary to secure the benefits of free consultation and discussion, and to guard against too easy a combination for improper purposes; as, on the other hand, the number ought at most to be kept within a certain limit, in order to avoid the confusion and intemperance of a multitude. In all very numerous assemblies, of whatever character composed, passion never fails to wrest the sceptre from reason. Had every Athenian citizen been a Socrates, every Athenian assembly would still have been a mob.
Put another way, if this amendment were to pass, we'd have a mob and not a Congress. (Hecklers, I hear you.)
The "constitutional crisis" that would ensue would most likely follow a very predictable trajectory. SCOTUS would need to reconcile the two, and the above paper would be brought up. The originalists would point to this paper and say that the 1911 Act was probably more in keeping with what the founders meant by the amendment, and then everybody would figure out a compromise. With the prospect looming of fitting nearly 1700+ members into the Capitol and 435 Congressmen fearing they'll lapse into irrelevance, "something" would get done - but then you get so hypothetical that is would be nearly impossible to determine.