According to Regulation 45, contracting authorities may accept (or even require) economic operators to submit variant proposals. The possibility of using variants is not new and has been around in public procurement for a long time but has never been very popular or widespread. Regulation 45 does not provide any novelty that will anticipate a change in practice. Albert's comments on Regulation 45 are here.
Paragraph 2 and 3 state the obligation of mentioning if variants are to be accepted either in the contract notice or the invitation to tender, thus ensuring economic operators are informed of this possibility before starting to prepare their tenders.
As accepting variants implies that the tenders being submitted may be very different from one another, the contracting authority is under the obligation to provide the minimum requirements which shall be common to all tenders (paragraph 4) as well as award criteria that are broad enough to encompass the variants (paragraph 5). This is naturally more difficult to achieve than a straight comparison with narrow and detailed technical specifications and can explain the reticence by contracting authorities in using variants. Contracting authorities want to reduce complexity, time involved in assessing tenders and obviously risk as well, as if the award criteria and minimum requirements are not set well, they may face incomparable tenders. It can be argued however that good functional specifications would naturally facilitate the use of variants (by establishing the objectives/outputs and not the means) but those are also quite uncommon across the EU as well.
Contracting authorities keep complaining about the lack of flexibility of procurement rules, but the truth is there is plenty of flexibility for people that understand the rules and have the right skills. If what perhaps is meant in those "lack of flexibility" comments is "we cannot just pick who we want", then yes, that kind of "flexibility" is not really permitted under the rules.
Finally, paragraph 7 states that in case variants are accepted, then the classification of the contract as either supplies or services, cannot be used to exclude a tender that offers the other. In other words, the definition of a contract as a supply or services contract cannot be used as a minimum requirement.