Do buyers and sellers use the same valuation models?

In theory, there is no reason for an investor to prefer such or such valuation model on the basis of whether he is a buyer or a seller.
In practice, however, a certain hierarchy of valuation models has arisen. A seller generally prefers discounted cash-flow (DCF), as it is based on a business plan that is seldom pessimistic and which should therefore be scrutinised closely. The business plan has been put together by the target company's management, but most often on instructions from the selling shareholder in order to obtain a higher valuation. However, while he is talking all about DCF, the seller is actually thinking about peer multiples (either market multiples or transaction multiples), as:

The buyer, on the other hand, bases his negotiations on peer comparison, as this could result in a lower price than a DCF valuation. The argument often made is that other buyers have paid this price and not 130% or 140% this price. However, while talking about peer comparisons, the buyer is actually thinking DCF, as the future profitability of the acquisition will depend on his post-takeover battle plan (synergies, new developments, etc.). Hence, the value from a DCF applied to a business plan that he believes is "realistic" is in fact the price that he can pay without destroying value for his shareholders.
Once multiples enter the fray, seller and buyer will begin debating methodology like two Baptist preachers quoting Scripture. The choice of peer sample is especially ticklish1, and such discussions are seldom very productive...
A DCF model, however, will necessarily require a discussion of the target's business plan. This negotiation of substance will be much more interesting than technical jousting on cost of capital or terminal value, say, or other issues.

(1) A footnote: we once heard of a seller's financial advisor refuse to include a company in the sample just because it was Danish! Something indeed was something rotten in Denmark ...