This is an interesting issue as the Yaesu FT-817 is basically the definition of portable QRP transcievers, and the Elecraft KX3 is one of the hottest ones out there at the moment, offering a very high-performance reciever in a small and medium-priced package due to SDR-based technology, wich is one of my main interests in ham radio.
The first issue one might look at is the price point; an assembled Elecraft KX3 + MH3 microphone + KXBC3 charger is US$ 1120, a standard FT-817ND already comes with mic, charger, battery and an antenna for about US$ 600. An external tuner is an option for both for about the same price, but the KX also has the option of an internal tuner. If you like to mess around with electronics, have some spare time and want to save about US$100 on the KX3, you can get it as a kit and assemble it yourself.
Because the two represent different generations of ham radio technology, the performance in the newer KX3 is undeniably better than what you can get with the older 817. Actually, the reciever in the Elecraft KX3 is so good that it ranks among the top ones available today, beating transcievers that cost 2-3-5 times more. It's user interface is richer, with an actually usable display and alot of buttons available for direct control. It is also newer, has the internal tuner option and offers a bit more power (10W instead of 5W).
The Yaesu FT-817ND is simpler, it's reciever is just "OKish" (and rather noisy on 2m/70cm bands) and has been plagued with the delicate finals issue. It is a bit heavier (1.2Kg vs 0.7Kg), the display is not useful at all, the S-meter is more of an on/off type and it has much less buttons, being more menu-driven.
Both target the portable operations crowd, where lightweight, simplicity and reliability are the key factors. Therefore, the 817's modest interface becomes a plus, the small screen and the few low-profile buttons are much less likely to be damaged while you carry it in the backpack together with a larger baterry, tools or portable atennna parts; it is almost bulletproof in the field compared to the high-tech fragile KX3 that has connectors sticking out on all sides, fancy buttons and the big frontal LCD. The FT-817's extra weight is there because of the internal rechargeable battery wich the KX3 doesn't have (but you can add), and the SDR DSP-based reciever in the KX3 is most of the time worthless in a situation where you are struggling to be heard. Noisy 2m/70cm reciever you say ? Might be, but the KX3 doesn't cover those bands at all. And if you worry so much about the sensitive finals on the baby Yaesu, you can buy two 817's for the price of one KX3 and keep them both with you in the field, you can even use one as a second reciever wich is much more useful than 100dB 2KHz spaced dynamic range. If you need a rough and proven do-it-all portable transciever, the 817 is still the best match, even after 12 years.
Adjustable power up to 10W from a reliable final unit (unlike the Yaesu's), low recieve consumption and the internal tuner option are nevertheless key features for a portable that overall prove Elecraft has good engineers, unfortunately not complemented by a good and clear concept to work on. I don't really find the target for the KX3, it's layout is not the best for portable, the performance is awesome but over the US$ 1k people would expect 100W from a base station unit and the connector placement would make a mess of your mobile installation. The IC-703 showed Icom understood pretty well what the FT-817 lacked, Elecraft should've picked up something from them.