PE entry multiples - pre or post on enterprise value

i presume your question means transacted comps (post-money) vs trading comps (pre-money).

It is not "preferred" per se, it is just another data point for the valuer - knowing what other people have paid for similar companies is very useful in your valuation.

In any real work though, you would use trading comps, transacted comps and DCF to value a company. Thereafter, you would have a range of prices that you know is reasonable to purchase the company for.

If you REALLY want to justify that it is better, then take this analogy - When buying a second-hand Honda Accord on the market, you know the list price of it (trading comp). However, this may be drastically different from the amount someone actually paid for it (transacted comp) - other buyers may have negotiated the prices down etc., so the actual price is lower*. As a buyer, it is more helpful to you to know the transacted price.

*In a scenario with companies, the transacted comp is usually higher than the trading comp because of the control premium one would have to pay.