There was a decision in that case recently. The court held that it is no violation of the DMCA to market a transmitter that is compatible with the garage door opener of a competitor.
That's good news. Deciding the other way round would open the door to abuse the DMCA for the purpose of restricting competition in markets unrelated to copyrighted works. That door should stay shut, not the garage doors of consumers.
How would European law handle this case?
One relevant text might be the 2001 Internet copyright directive, which is somewhat of an European DMCA. However, that directive states in recital 50:
"(50) Such a harmonised legal protection does not affect the specific provisions on protection provided for by Directive 91/250/EEC. In particular, it should not apply to the protection of technological measures used in connection with computer programs, which is exclusively addressed in that Directive. It should neither inhibit nor prevent the development or use of any means of circumventing a technological measure that is necessary to enable acts to be undertaken in accordance with the terms of Article 5(3) or Article 6 of Directive 91/250/EEC. Articles 5 and 6 of that Directive exclusively determine exceptions to the exclusive rights applicable to computer programs."
So the 2001 directive is not applicable, since the Skylink case is about access to a computer program.
And the 1991 directive says in Article 5 Section 1:
1. In the absence of specific contractual provisions, the acts referred to in Article 4 (a) and (b) shall not require authorization by the rightholder where they are necessary for the use of the computer program by the lawful acquirer in accordance with its intended purpose, including for error correction."
That gives the garage owner in this case the right to do everything necessary to actually use the program he has bought and paid for. The intended use of the program is opening the garage door. Doing that requires a transmission, so operating the transmitter is "necessary".
That means that the transmitter is not a "means" under Article 7 Section 1 (c), reproduced below. The garage owner is authorized to open the garage. A burglar would be unauthorized. If the transmitter enabled unauthorized burglars to open garages, it might be prohibited, if that is the "sole intended purpose".
1. Without prejudice to the provisions of Articles 4, 5 and 6, Member States shall provide, in accordance with their national legislation, appropriate remedies against a person committing any of the acts listed in subparagraphs (a), (b) and (c) below:
(a) any act of putting into circulation a copy of a computer program knowing, or having reason to believe, that it is an infringing copy;
(b) the possession, for commercial purposes, of a copy of a computer program knowing, or having reason to believe, that it is an infringing copy;
(c) any act of putting into circulation, or the possession for commercial purposes of, any means the sole intended purpose of which is to facilitate the unauthorized removal or circumvention of any technical device which may have been applied to protect a computer program."
In conclusion, I think that European law would come to the same result. You can't stop competition in markets unrelated to the market for a computer program by pointing to the copyright on that program.