An auction house or dealer will of course charge commission. However if they are specialists in musical instruments they will be able to advise on realistic values and realistic reserve prices, and should advertise the instruments more effectively. If they do their job properly then there is a good prospect of getting a better price than you might privately. They will also take responsibility for dealing with buyers who don't go ahead, rather than you having to deal with ebay/paypal's disputes process.

Having said that, auctions are unpredictable and results can be surprising or disappointing, depending on who is in the room on that day. However a sensible reserve price should avoid selling at too low a price.

Also, disposing of a collection of this size privately will involve a lot of time and hassle (at a time when no doubt there are lot of other things to deal with) which selling through a dealer would avoid.

I would be very wary about selling a valuable instrument through ebay/paypal after reading this:

Paypal destroys mislabelled violin

although mislabelling and incorrect attribution of guitars is probably less of an issue than with violins.

Valuations for insurance shouldn't be relied on. They are invariably higher than market prices as they reflect the additional costs that may be incurred in finding a similar replacement.