tl;dr
When calling the PowerShell CLI (powershell.exe for Windows PowerShell, pwsh for the cross-platform PowerShell [Core] 6+ edition):
- Using embedded - "in an overall- "..."string comes with escaping challenges.
 
- If feasible for a given command, formulating it without embedded - "is the easiest solution:
 
powershell -Command "Compare-Object (Get-Content tex1.txt) (Get-Content tex2.txt) | Where-Object {$_.SideIndicator -eq '<='} | select inputobject |  ft -hidetableheaders"
Read on, if you do need to use embedded ".
eryksun points out that your problem is your lack of escaping of embedded " chars. inside the overall "..." string, which causes cmd.exe to see multiple strings, including parts it considers unquoted, which causes problems with special characters such as | and < - they never reach PowerShell.
Nesting double-quote strings from cmd.exe is tricky business:
- To make cmd.exehappy, you need to double the embedded"chars. ("")
- Separately, to make powershell.exehappy, you need to\-escape"chars.
- Note: PowerShell [Core] 6+, the cross-platform edition, on Windows now also accepts ""by itself, which is the most robust choice.
 
Generally, dealing with quoting and escaping arguments when calling from cmd.exe is a frustrating experience with no universal solutions, unlike in the Unix world. Sadly, PowerShell has its own challenges, even in the Unix world.[1]
In short: Escape embedded " chars. when calling the Windows PowerShell CLI, powershell.exe, from cmd.exe as follows (for the PowerShell (Core) 7+ CLI, pwsh.exe, "" is the robust choice):
- Use - "^""(sic) when using- powershell.exe -Command, which works robustly.
 - 
- Caveat: "^""does not work for calling other programs.
- This saves you from additional escaping, as would be necessary if you used \"
- Example: powershell -command " Write-Output "^""a  &  b"^"" "yieldsa  &  b, as expected, and the&didn't need escaping.
 
- If you use the simpler - and customary - - \", you may need to perform additional escaping: Specifically, you must individually- ^-escape the following- cmd.exemetacharacters with- ^inside- \"...\"runs:- & | < > ^Thanks, LotPings.
 - 
- Example: powershell -command " Write-Output \"a  ^&  b\" "yieldsa  &  b; that is, the&needed escaping with^.
 
- Additionally, to treat - %(and, with- enabledelayedexpansion,- !) verbatim, the escaping syntax unfortunately depends on whether you're calling from the command line or a batch file: use- %^USERNAME%(- !^USERNAME) from the former, and- %%USERNAME%%(- ^!USERNAME^!/- ^^!USERNAME^^!inside- \"...\"runs) from the latter - see this answer for the gory details.
 
It is unfortunate that cmd.exe makes use of \" treacherous, given that it is supported by virtually all programs (except batch files), and if it weren't for these extra escaping requirements, command lines that use it have the potential to work across different platforms and shells - with the notable exception of calling from PowerShell, where, sadly, an additional layer of escaping is needed and " inside "..." must be escaped as \`" (sic); see this answer.
See the bottom section for ways to ease the escaping pain by avoiding use of nested ".
Other programs, including PowerShell Core:
- Use just - ""for programs compiled with Microsoft compilers and, on Windows, also Python and Node.js as well as PowerShell Core (- pwsh.exe).
 Regrettably, this robust option does not work with- powershell.exe, i.e. Windows PowerShell.
 
- Use - \"for programs with Unix heritage, such as Perl and Ruby - which comes with the escaping headaches discussed above.
 
Avoiding embedded ":
When you call PowerShell's CLI, you can often get away without needing to embed double quotes:
- There may be arguments in your string that don't require quoting at all, such as - text1.txtand- text2.txt
 
- You can alternatively use single-quoting (- '...') inside the overall command string, which require no escaping; note that such strings, from PowerShell's perspective, are string literals.
 
To put it all together:
powershell -Command "Compare-Object (Get-Content tex1.txt) (Get-Content tex2.txt) | Where-Object {$_.SideIndicator -eq '<='} | select inputobject |  ft -hidetableheaders"
Note that I've also removed the & { ... } around your command, as it isn't necessary.
[1] eryksun puts it as follows: "This is the inescapable frustration of the Windows command line. Every program parses its own command line, using whatever rules it wants. So the syntax of a command line has to work with not only the shell (CMD) but also all programs invoked in the pipeline. In the Unix world the shell parses the command line into argv arrays, so typically you only have to get the syntax right to make the shell happy."
The problems with PowerShell Core, even on Unix, stem from how it re-quotes arguments behind the scenes before passing them on - see this GitHub docs issue.