If "protection" means you have the right to exclude others from making, selling, importing, using, etc., then you have no protection until a patent issues. That might take a couple of years after filing a non-provisional utility patent application.
If "protection" means you have a stake in the ground of a date that no one who files after you do can beat, then either filing gives you equal protection for the subject matter it properly covers. (Although that will only last a year if a non-provisional.) In many cases, what might be filed as a provisional application is less detailed or complete than something that might be filed as a non-provisional application. Therefore a typical provisional might be less protective merely due to level of effort put into it. If the fact that the cost for both is the same means the content would be identical then the protection of having a particular filing date would be identical either way.
I hope the terms you are using are not the terms your attorney is using. The two types of application you are considering are technically a provisional utility application and a non-provisional utility application. They are both utility application as opposed to design or plant patent applications. This might seem pedantic but patent law is an area that spits hairs and has bad consequences when details are not correct.
If the actual application content is identical then the difference is a few hundred dollars in lower filing fees now for the provisional and a delay in getting a granted patent. If you will definitely be moving ahead to later also file a non-provisional than the non-provisional filing fees are just an added cost to what will be the total costs after both are eventuality filed.
One good reason to file a provisional is that you get today's priority date for what you have developed so-far and also get a year to come up with improvements and alternate embodiment that will be added to make your non-provisional filing. If that happens, presumably, it will cost another 2K to write that new document.
If asked to draft a provisional, some patent practitioners will consider that they are being asked to do a less thorough job compared to drafting a non-provisional and will charge less to draft the provisional. Others will only draft a non-provisional quality application whether you want to file as a provisional or a non-provisional and charge the same. You are being charged the same either way but you might ask if the effort and end-product would be exactly the same.
And $2k is low for a typical non-provisional to be drafted and filed.