Both are well-established dealers of original props.
ScreenUsed has an excellent reputation in the original prop community. Though I haven't purchased anything from them myself yet, I absolutely would not hesitate to deal with Desi and Jeff. They also do some lovely custom displays.
Premier Props is primarily a studio reseller. They deal in a pretty high volume of pieces, some of them more significant than others. I have heard other collectors relate stories of less than perfect customer service, and I have seen a thing or two misidentified, though I cannot recall ever hearing of any authenticity challenges. I've purchased from them and have had no issues personally.
There are a number of other good, reputable dealers out there. I'll mention the
Prop Store of London as one of the larger ones (especially since they are an affiliate of this board). I've dealt with them several times and they are top notch.
As far as a "safe bet" goes...I will say that there are no absolutes. Even a good dealer can make mistakes. There are also bad dealers who are out to intentionally defraud buyers. Always, always be as informed as possible about your purchases, ask plenty of questions and do as much of your own research as you can. There are pitfalls to buying original props, and missteps can be pretty expensive. You can save yourself a lot of potential disappointment by educating yourself before you buy. There have been lawsuits filed over issues as simple as someone not fully understanding terminology (i.e. made for production vs. screen used).
I personally found jdebord's
Original Prop Blog to be a great resource for someone starting out in collecting original props. He's written some excellent articles for those interested in learning more about the hobby.
