Differences between H81-plus and a Z87

Z87
The Z87 chipset is the most feature-rich chipset and is the only one to offer full CPU overclocking for supported (K-series) processors. This chipset can easily handle SLI/Crossfire configurations by allowing the 16 PCI-E lanes from the CPU to be divided into either a single x16 slot, dual x8 slots, or a single x8 plus two x4 slots. While this means that the Z87 chipset can support triple SLI/Crossfire configurations, we typically recommend against doing so except in isolated circumstances. In most cases a Socket 2011 system is a better option as the additional PCI-E 3.0 lanes will provide improved performance.
As far as its feature set goes, Z87 supports Rapid Storage Technology, Smart Response Technology (otherwise known as SSD Caching), six SATA 6Gb/s ports and six USB 3.0 ports. In addition, Z87 also supports Lake Tiny which provides increased SSD power optimization features when using Smart Response Technology (SSD Caching). Finally, it supports two DIMMs per memory channel so it will be able to utilize up to four sticks of RAM.
The Z87 chipset is the chipset for the user that wants it all. CPU overclocking, support for triple SLI/Crossfire, plenty of SATA 6GB/s and USB 3.0 ports, and plenty of additional features.

H81
The H81 chipset is the "budget" option and as such is very limited compared to the other consumer chipsets. It does not support SLI/Crossfire at all, has only two SATA 6Gb/s ports (plus four SATA 3Gb/s ports), and only two USB 3.0 headers. In addition, it does not support any of the major features found in the other chipsets like RST12 and Smart Response Technology. Finally, H81 only supports one DIMM per memory channel so it will be limited to a maximum of two sticks of RAM.
H81 is a great option for small form factor systems where you rarely have more than one discrete card and a couple of SATA drives. For larger desktop systems, we recommend avoiding the H81 chipset and using either Z87 or H87 instead to allow for the possibility of future upgrades.

Go with Z87, will be the best for you in gaming build.

Source: http://www.pugetsystems.com/labs/articles/Z87-H87-H81-Q87-Q85-B85-What-is-the-difference-473/#ConsumerChipsets%28Z87,H87,H81%29