Modchips override your BIOS with a different one, allowing for unsigned code (i.e homebrew apps/emulators/dashboards) to be run.
A TSOP flash replaces your BIOS with a different one, allowing for unsigned code to be run.
No you do not need a modchip to do a TSOP flash. You need at least a softmodded console in order to do it though because the programs used to overwrite the onboard BIOS are unsigned.
I personally have never used a modchip just because you get almost the same effect by doing a TSOP flash. It free and in my opinion looks to be easier than installing a modchip.
You can change the boot screen, and there are a few other perks like not having to use a locked hard drive and being able to boot a home made CD-rom in case something goes wrong with your console. If something goes wrong with your softmod and you don't have the right files backed up, you can be locked out of your xbox. With a custom bios (either by TSOP flash or modchip) you can fix mistakes a lot easier.
Here's an example of a few perks provided by iND-BIOS 5003
Boot All Originals
Boot All Unsigned Code
Boot All Backups
No DVD Rom Hack
Auto Load DVD Disable/Enable
Boot with corrupted eeprom
Custom error screen
Auto clock set
On the fly .xbe patching:
--Xbox LIVE Block
Hard Drive Swap Hack
No AV Cable Hack
In Game Reset - Off/Quick/Complete
--Reset to Game/Reset to Dash (Triggers + Black + Back) OR (Triggers + Back + Start)
--Shutdown (Triggers + Back + White)
--Tray Eject (Triggers + Right Thumb + Dpad UP)
--Tray Close (Triggers + Right Thumb + Dpad DOWN)
--Power Cycle (Triggers + Back + X + Black) [hint: hit X before black]
Configurable bios intro:
---Custom Flubber, loads from c:\flubber.x or user specified file
---Flubber, glow, scene(3), fog colors
---Camera angle (15 choices)
---Spikey and/or Wireframe blob
---Custom "X" logo, loads from c:\xlogo.x or user specified file
---The 'normal' hacks: lip, lip highlights, inner walls, inner glow
---Enable/disable light (the white light coming in from the top right)
---Replace "XBOX" text with "IND-BIOS"
---Custom "XBOX" text, loads from c:\text.x or user specified file
---XBOX text color
---Change Background color
---Custom "Microsoft" logo, loads from c:\mslogo.bmp
Configurable LED color
Configurable fan speed
Configurable boot sequence
Configurable MAC address
Use e:\dashboard.xbx (optional) - used to specify a dash to boot for debug
Will boot some BFM bioses from e:\xboxrom.bin (make sure you can recover
if you try this)
hope that helps