Why is it faster to run a query via a linked server?

Question

I have this query that a vendor wants to start running on my data warehouse. The version I'm posting runs at 18 seconds if I run via a linked server (SQL Server 2017, 12GB RAM, more CPU) as a remote query, and 4 minutes if I run it directly on the server (4GB RAM, SQL Server 2008).

Yes, I know my servers suck. We are getting a better set.

Question: Why would it be faster to run this:

 select * from [eih-dr01].livefdb.[dbo].[RegAcct_Main]

than going directly onto the server eih-dr01 and running this:

 select * from RegAcct_main

Here's the big, bad query, for reference:

 declare @start datetime 
 set @start = dateadd(minute, -45, getdate())
 SELECT 
 'AST' AS [HDR]
 ,RAM.Facility_MisFacID AS [FID]
 ,MRN.PrefixMedicalRecordNumber AS [MRN]
 ,RAM.AccountNumber AS [VISIT_NBR]
 ,MDSM.[Name] AS [CATEGORY]
 ,PADM.MisDocumentationSectionOid AS [CATEGORY_ID]
 ,MQM.Text
 ,MDSQ.QuestionMnemonic
 --,COALESCE(MQM.Text,MDSQ.QuestionMnemonic) AS [QUESTION]
 ,PADQ.QueryValue
 --,REPLACE(REPLACE(REPLACE(REPLACE(PADQ.QueryValue,'|}',''),'{',''),'}',''),'|',',') AS [FINDING]
 ,PADM.DateTimePerformed
 --,CONVERT(VARCHAR,PADM.DateTimePerformed,101) + ' ' + LEFT(CONVERT(VARCHAR,PADM.DateTimePerformed,108),5) AS [REPORT_DT]
 --,PADM.DateTimePerformed
 --,1 AS Ord
 FROM [eih-dr01].livefdb.[dbo].[PcsAcctAct_IntActAssessments] PAAIAA
 INNER JOIN [eih-dr01].livefdb.[dbo].[RegAcct_Main] RAM
 ON PAAIAA.SourceID = RAM.SourceID
 AND PAAIAA.VisitID = RAM.VisitID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[MisFac_Main] MFM
 ON RAM.SourceID = MFM.SourceID
 AND RAM.Facility_MisFacID = MFM.MisFacID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[MisHimDept_Main] MHDM
 ON MHDM.SourceID = MFM.SourceID
 AND MHDM.MisHimDeptID = MFM.HimDepartment_MisHimDeptID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[HimRec_MedicalRecordNumbers] MRN
 ON RAM.SourceID = MRN.SourceID
 AND RAM.PatientID = MRN.PatientID
 AND MHDM.MedicalRecordNumberPrefix = MRN.MrnPrefixID
 INNER JOIN [eih-dr01].livefdb.[dbo].[PcsAssmntData_Main] PADM
 ON PAAIAA.SourceID = PADM.SourceID
 AND PAAIAA.VisitID + '{A^' + PAAIAA.InterventionActivityAssessment_MisDocSectID + '}' = PADM.PcsAssmntDataID
 AND PAAIAA.InterventionActivityUrnID = PADM.IdentifierID
 INNER JOIN [eih-dr01].livefdb.[dbo].[PcsAssmntData_Queries] PADQ
 ON PADM.SourceID = PADQ.SourceID
 AND PADM.PcsAssmntDataID = PADQ.PcsAssmntDataID
 AND PADM.IdentifierID = PADQ.IdentifierID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[MisDocSect_Main] MDSM
 ON PADM.SourceID = MDSM.SourceID
 AND PADM.MisDocumentationSectionOid = MDSM.MisDocSectID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[MisDocSect_Questions] MDSQ
 ON PADQ.SourceID = MDSQ.SourceID
 AND PADQ.QuerySetID = MDSQ.QuestionSetUrnID
 AND PADQ.QueryNumberID = MDSQ.QuestionUrnID
 AND PADM.MisDocumentationSectionOid = MDSQ.MisDocSectID
 LEFT JOIN [eih-dr01].livefdb.[dbo].[MisQry_Main] MQM
 ON MDSQ.SourceID = MQM.SourceID
 AND MDSQ.QuestionMnemonic = MQM.MisQryID
 where 
 --RAM.AdmitDateTime 
 PADM.DateTimePerformed >= @start
 --and MDSM.[Name] = 'Vital Signs'
 and PADM.MisDocumentationSectionOid like '%VS%'

• LowlyDBA - John M: Perhaps some of the things in this question apply to your situation? Check out the execution plans and add them to the question (pastetheplan.com)
• Erik Reasonable Rates Darling: Distributed Query Deep Dive - Conor Cunningham has a lot of good information in it about how and where remote queries are processed. It's possible that the majority of the hard work is done on the better-equipped server. It may also be a Cardinality Estimation and plan choice issue. Without the query plans, it's impossible to say. Like asking why you eat pizza faster left handed.
• stacylaray: Check out dba.stackexchange.com/questions/77875/… It could be spending the extra time rendering the results on the resource limited server.