The new Catalyst 3560-X and 3750-X switches are business class models of standalone (3560X) and stackable(3750X) switches for the aggregation and access network layers. Cisco’s latest innovations deliver new features  like full Power over Ethernet (POE+), redundant power supplies, and Cisco StackPower  on the 3750-X,  features which are unavailable on the 3560-E, 3750-E and 3560G, 3750G models.
The Basics
Power over Ethernet Plus
The Catalyst 3750-X and 3560-X switches deliver PoE+ for a maximum power of 30W per port.  The switches support both PoE standards, 802.3af and 802.3at, which define power maximums for an Ethernet a port.
Redundant Power and Fans
The Cisco 3560-X and 3750-X support dual redundant power supplies and fans. Redundant fans come standard.  Four power supply options are available including a DC power supply for PoE.  Only one power supply is required to run a single switch except when full PoE+ is deployed on a 48-port switch.
Power sharing capabilities
The Cisco StackPower can be deployed in three configurations: power-sharing mode, redundant mode, and RPS mode.  Power-sharing mode aggregates and shares power within the switch stack.  Redundant mode sets aside power from the stack for a 1+N redundancy.  RPS mode is a one to one (1:N) redundancy with a designated power supply as backup. StackPower is limited to four switches in a ring topology.
StackWise Plus
Like StackWise technology,  StackWise Plus enables the configuration of up to nine 3750 and 3750-X switches into a single logical switch.  The stack promotes a single switching unit managed by a main switch which automatically works and updates all optional routing tables and switching. This feature is not available in 3560X
One surprising difference is that the 3750-X switch provides only 64 Gbps of backplane throughput whereas the older 3750-E delivers 128Gbps.  As an alternative, the Juniper EX4200 has 128Gbps performance and can have ten switches in a virtual switch configuration for a total of 480 ports.

The 3560-X and 3750-X are standard Layer 2 switches which can be upgraded to Layer 3.  This licensing option represents a cost. 

3560-X and 3750-X models have a strong limited lifetime warranty that includes next business day replacement and 90 day access to Cisco TAC. Most competitive switch offerings have the NBD replacement as a chargeable support option.