I agree with the general consensus here that there probably isn't a great deal of meaningful semantic distinction between Χριστὸς Ἰησοῦς and Ἰησοῦς Χριστὸς. However, there's an incidental morphologic irregularity that explains at least some of the variation.
In NT Greek, the dative form of Ἰησοῦς is Ἰησοῦ, identical in form with the genitive.1 This leads to a degree of ambiguity in syntactic environments where either case is possible. On the other hand, χριστός is fully declinable. All else being equal, speakers and writers of a language naturally tend to minimize ambiguity. Where we have Ἰησοῦ, which looks like a genitive, acting as a dative, it's helpful to have something before it to alert us to the fact that it's really dative. Χριστῷ fits the bill.2
Here are the statistics:3
The largest discrepancy in prevalence between Χριστὸς Ἰησοῦς (XI) and Ἰησοῦς Χριστὸς (IX) occurs in the dative: 10:1 in favor of XI, in contrast to an overall preference for IX. Furthermore, in 4 of the 5 cases of the dative Ἰησοῦ Χριστῷ, another appositive dative immediately precedes, resolving the ambiguity.4 This pattern suggests to me that the selection of either Χριστὸς Ἰησοῦς or Ἰησοῦς Χριστὸς in the NT was frequently motivated by a (no doubt unconscious) tendency to introduce the phrase with a syntactically unambiguous form.5
1. It is a common feature of proper nouns (and rare among common nouns) to be only partially or not at all "declinable." In the NT, we have: Ἰησοῦς (nom), Ἰησοῦ (gen, dat, voc), and Ιησοῦν (acc). Interestingly, the LXX has a distinct form Ἰησοῖ which is most often used for the dative when referring to Ἰησοῦς the "assistant" of Moses.
2. For the purpose of syntax, the phrases Χριστὸς Ἰησοῦς and Ἰησοῦς Χριστὸς function basically like two appositive nouns, i.e., both words are always in the same case. For more on what the word Χριστὸς is really doing there, see Title of Christ? on Christianity.SE.
3. Using the text of NA-28 with Accordance software; morphologic tagging by William D. Mounce and Rex A. Koivisto, 2013.
4. In three cases that noun is κυρίῳ, the dative of κύριος ("lord"; 1 Thes 1:1, 2 Thes 1:1, 2 Thes 3:12). In 1 John 5:20, we have ἐν τῷ υἱῷ αὐτοῦ Ἰησοῦ Χριστῷ; the preposition, the article, and υἱῷ all divulge the case of Ἰησοῦ. The single exception is Jude 1: τοῖς ἐν θεῷ πατρὶ ἠγαπημένοις καὶ Ἰησοῦ Χριστῷ τετηρημένοις. Here one really needs to wait for Χριστῷ to figure out what's going on unless, as suggested in BDAG, "the ἐν before θεῷ is to be repeated."
Not surprisingly, when Ἰησοῦ as dative is used without Χριστῷ (37x), the language finds other unambiguous dative markers. It is almost always preceded by the article (31x) or an appositive (3x κυρίῳ, 1x μεσίτῃ). The exceptions are Rev 1:9 (but ἐν requires dative) and 2 Cor 4:14 (but σὺν requires dative).
5. For the null hypothesis that word order is independent of case (dative vs non-dative): χ2 = 72.7045, p < .00001.