i have never used an hdmi splitter myself. never had the need really. but i have used other splitters for various video sources over the years. generally the ones that worked the best were amplified and not passive. meaning they plug into an outlet to keep the signal boosted to both outputs (or more if it has more), a signal can get weaker as it is split and the length of the cables can also degrade the signal. i assume these tv's won't be right next to each other!!
i'd look for a decent amplified splitter and you should be ok. for me i tend to avoid the cheapest ones i find but skip over the crazy expensive ones as well. something right in the middle from a brand you recognize is usually good enough for me. hope this is helpful, never used an hdmi splitter but have used vga, cable, directv, sound and other splitter types along these lines. the amplified ones always seemed to offer the best experience.